The Robert Smyth School
Mathematics Faculty
Topic 9
Solving Equations 2
Innovation & excellence
HW5 – Grade A
Shading Regions
1.
(a)
List the integer values of n such that 3  3n < 18
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Answer ...............................................................
(3)
(b)
y
4
Q
3
2
1
0
P 0
(i)
1
2
3
4
5
6
x
Find the equation of the line PQ.
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Answer ...............................................................
(1)
(ii)
Write down three inequalities which together describe the shaded area.
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Answer ...............................................................
(3)
(Total 7 marks)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Topic 9
Solving Equations 2
Innovation & excellence
2.
(a)
3x – 5  5 – 2x
Solve the inequality
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Answer .......................................................
(2)
(b)
The region R is shown shaded below.
y
4
3
2
1
–4
–3
–2
–1
O
1
2
3
4
x
–1
–2
–3
–4
Write down three inequalities which together describe the shaded region.
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Answer .......................................................
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(3)
(Total 5 marks)
The Robert Smyth School
2
The Robert Smyth School
Mathematics Faculty
Topic 9
Solving Equations 2
Innovation & excellence
3.
On the grid below, indicate clearly the region defined by the three inequalities
y  4
x  –3
y  x2
Mark the region with an R.
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y
6
5
4
3
2
1
–6
–5
–4
–3
–2
–1 O
1
2
3
4
5
6
–1
–2
–3
–4
–5
–6
(Total 3 marks)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Topic 9
Solving Equations 2
Innovation & excellence
4.
On the grid below, indicate clearly the region defined by the three inequalities
x1
yx–1
x+y7
Mark the region with an R.
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y
8
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
x
(Total 3 marks)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Topic 9
Solving Equations 2
Innovation & excellence
1.
(a)
1n<6
M1
oe
(b)
1
2
3
4
5
A1 for 4 correct or if 6 included
–1 for each extra number
(i)
y=
(ii)
y0
1
x
2
oe
x6
y
A2
Accept y > 0 or 0  y  3
Accept x < 6 or 0  x  6
1
x
2
ft their (b)(i)
1
Accept y < x or x  2y oe
2
SC1 all 3 boundaries given as equations
SC2 all 3 boundaries given as inequalities the wrong
way round
B1
B1
B1
B1 ft
[7]
2.
(a)
5x  = 10
x=2
(b)
y2
x  –3
Allow 5x  10 for Ml, and 5x = 10 only if inequality recovered
M1
SC1x2
Accept –3  y  2, < for 
Accept –3  x  2, < for 
yx
B1
B1
B1
oe Accept y > x
Note penalise poor notation first time only
[4]
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Topic 9
Solving Equations 2
Innovation & excellence
3.
All 3 lines correct.
R marked in correct region
Allow dotted lines
Special case if y ≤ 4 and x = – 3
drawn as y –3 and x ≤ 4 then this is
one error. So if region marked
correctly relative to these lines it is
B1 and if correct relative to y = x + 2
also it is B2
B3
R (= B2)
R (= B1) 4
–3
[3]
4.
Correct region indicated
Award marks dependent upon number of lines drawn correctly
and extent of shading
B3
[3]
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